6,818 research outputs found
The role of quantum recurrence in superconductivity, carbon nanotubes and related gauge symmetry breaking
Pure quantum phenomena are characterized by intrinsic recurrences in space
and time. We use such an intrinsic periodicity as a quantization condition to
derive the essential phenomenology of superconductivity. The resulting
description is based on fundamental quantum dynamics and geometrical
considerations, rather than on microscopical characteristics of the
superconducting materials. This allows for the interpretation of the related
gauge symmetry breaking by means of the competition between quantum recurrence
and thermal noise. We also test the validity of this approach to describe the
case of carbon nanotubes.Comment: Published version. Comments welcom
On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain
The continuous and discrete symmetries of the Kuramoto-Sivashinsky system
restricted to a spatially periodic domain play a prominent role in shaping the
invariant sets of its chaotic dynamics. The continuous spatial translation
symmetry leads to relative equilibrium (traveling wave) and relative periodic
orbit (modulated traveling wave) solutions. The discrete symmetries lead to
existence of equilibrium and periodic orbit solutions, induce decomposition of
state space into invariant subspaces, and enforce certain structurally stable
heteroclinic connections between equilibria. We show, on the example of a
particular small-cell Kuramoto-Sivashinsky system, how the geometry of its
dynamical state space is organized by a rigid `cage' built by heteroclinic
connections between equilibria, and demonstrate the preponderance of unstable
relative periodic orbits and their likely role as the skeleton underpinning
spatiotemporal turbulence in systems with continuous symmetries. We also offer
novel visualizations of the high-dimensional Kuramoto-Sivashinsky state space
flow through projections onto low-dimensional, PDE representation independent,
dynamically invariant intrinsic coordinate frames, as well as in terms of the
physical, symmetry invariant energy transfer rates.Comment: 31 pages, 17 figures; added references, corrected typos. Due to file
size restrictions some figures in this preprint are of low quality. A high
quality copy may be obtained from
http://www.cns.gatech.edu/~predrag/papers/preprints.html#rp
Characterization of the Crab Pulsar's Timing Noise
We present a power spectral analysis of the Crab pulsar's timing noise,
mainly using radio measurements from Jodrell Bank taken over the period
1982-1989. The power spectral analysis is complicated by nonuniform data
sampling and the presence of a steep red power spectrum that can distort power
spectra measurement by causing severe power ``leakage''. We develop a simple
windowing method for computing red noise power spectra of uniformly sampled
data sets and test it on Monte Carlo generated sample realizations of red
power-law noise. We generalize time-domain methods of generating power-law red
noise with even integer spectral indices to the case of noninteger spectral
indices. The Jodrell Bank pulse phase residuals are dense and smooth enough
that an interpolation onto a uniform time series is possible. A windowed power
spectrum is computed revealing a periodic or nearly periodic component with a
period of about 568 days and a 1/f^3 power-law noise component with a noise
strength of 1.24 +/- 0.067 10^{-16} cycles^2/sec^2 over the analysis frequency
range 0.003 - 0.1 cycles/day. This result deviates from past analyses which
characterized the pulse phase timing residuals as either 1/f^4 power-law noise
or a quasiperiodic process. The analysis was checked using the Deeter
polynomial method of power spectrum estimation that was developed for the case
of nonuniform sampling, but has lower spectral resolution. The timing noise is
consistent with a torque noise spectrum rising with analysis frequency as f
implying blue torque noise, a result not predicted by current models of pulsar
timing noise. If the periodic or nearly periodic component is due to a binary
companion, we find a companion mass > 3.2 Earth masses.Comment: 53 pages, 9 figures, submitted to MNRAS, abstract condense
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